[joshcohen]

Solomonoff induction is useful because without it there's no model of induction with infinite computational resources. "Logical induction" is not useful in the same way because without it we already have such a model: simply prove/disprove the propositions.

[Klaperman]

And what if the propositions we want to reason about are self-referencing or say something about the system itself in a Godelian way? You need probabilistic reasoning for that to actually work.

Also, "simply prove/disprove the propositions" requires infinite computational resources (we don't know how long the proofs will be or if there are any). Logical induction does not.